Question

If one root of the equation x² + px + 12 = 0 is 4, then the sum of the roots is ____________.

Answer 1

$$\begin{gathered} \mathrm{One}\mathrm{root}\mathrm{of}{x}^2+px+12=0\mathrm{is}4 \\ \mathrm{Let}\mathrm{us}\mathrm{suppose}\mathrm{the}\mathrm{other}\mathrm{solution}\mathrm{is}\mathit{}z. \\ \therefore \mathrm{Sum}\mathrm{of}\mathrm{roots}=\frac{-p}{1}=-p \\ \mathrm{i}.\mathrm{e}.z+4=-p \\ \mathrm{and}\mathrm{product}\mathrm{of}\mathrm{roots}\mathrm{is}12 \\ \mathrm{i}.\mathrm{e}.4z=12 \\ \mathrm{i}.\mathrm{e}.z=3 \\ \Rightarrow \mathrm{sum}\mathrm{of}\mathrm{roots}\mathrm{is}4+3=7 \end{gathered}$$